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Abstract
We define and study bivariant equivariant periodic cyclic homology for actions of
ample groupoids. In analogy to the group case, we show that the theory satisfies
homotopy invariance, stability, and excision in both variables. We also prove
an analogue of the Green–Julg theorem for actions of proper groupoids.
Keywords
cyclic homology, ample groupoids
Mathematical Subject Classification
Primary: 19D55, 55N91
Milestones
Received: 15 August 2025
Revised: 27 March 2026
Accepted: 13 April 2026
Published: 24 June 2026
© 2026 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers).
